The PS performance is typically quantified with a rate loss
rCL

Rloss (U,A) = H(A) - kn,

where \(R_{\mathrm {loss}} (\cdot ,\cdot )\)  denotes a rate loss in a sequence conversion, and \(R_{\mathrm {loss}}(U,A) \ge 0\)  for i.i.d. \(U_i\) .
The CCDM [1]}, which has been the state-of-the-art PS coding, has an almost negligible rate loss when \(n\)  is sufficiently large, e.g., 1000–10000.
The CCDM generates a fixed probability mass function (PMF) \(P_{A}\)  of output amplitudes \(A\)  regardless of the DM encoder input bit sequence and its statistics.
For a fixed PMF \(P_{A}\)  with a nonconstant-composition DM, \(U_i\)  is required to be uniformly distributed in general, which can be achieved by bit scrambling.
